1. Field of the Invention
The invention relates to methods and apparatus for sensing open phase, phase reversal, and voltage unbalance conditions in a polyphase source which supplies power to a polyphase load.
2. Description of the Prior Art
Polyphase electrical equipment is designed to operate on a balanced polyphase supply voltage. A balanced three-phase voltage is one in which the three phases are equal in magnitude, in proper phase sequence, and displaced from each other by 120.degree.. Open phase and phase reversals result in severe voltage unbalance between the phases of a polyphase source. These faults have long been detectable with various types of protection devices.
A condition which is much harder to detect, and which also poses a threat to electrical equipment, is moderate voltage unbalance between the phases of a polyphase source. This condition occurs in a three-phase source when all phases are present and in proper sequence, but differ in magnitude, or differ in phase by an angle other than 120.degree.. This condition, if not detected and controlled, can result in damage to electrical equipment, especially to electrical motors. Overload relays, which provide protection against large currents in electrical motors, may not be tripped by moderately unbalanced voltages, which can cause hot spots in the rotor of a three-phase induction motor.
A number of devices are known for detecting open phase, phase reversal and voltage unbalance conditions in a polyphase source and interrupting its connection to a load. These devices operate according to the theory of symmetrical components, which is well known to those skilled in the art. The theory of symmetrical components provides that any unbalanced polyphase system of vectors can be resolved by mathematical analysis into a balanced system of positive-sequence components, a balanced system of negative-sequence components and a unitary system of zero-sequence components having the same phase and magnitude.
Voltage unbalance can be determined from these components as follows: EQU % Voltage unbalance=([V.sub.2 ]/[V.sub.1 ]).times.100%
where:
[V.sub.2 ]=the magnitude of a negative-sequence component derived from a three-phase voltage, and PA1 [V.sub.1 ]=the magnitude of a positive-sequence component derived from the same three-phase voltage.
Because the magnitude of the components within either the positive- or negative-sequence system are the same, any one of the components from each system may be used for V.sub.1 and V.sub.2, respectively. When a three-phase voltage is balanced the magnitude of any of the negative-sequence components is zero, and the positive-sequence components equal the single-phase voltages. As the percentage of unbalance increases, the magnitudes of the negative-sequence components increase while the magnitudes of the positive-sequence components decrease. The magnitudes of the negative-sequence components have been found to be related to the heating that occurs in the rotor of an induction motor under unbalanced conditions. In view of this relationship, one of the negative-sequence components may be compared with some fixed reference, such as line voltage, instead of a positive-sequence component in judging the potential harm of voltage unbalance.
The negative-sequence components can be obtained mathematically by multiplying vectors representing the line voltages or line currents by a phase shift operator. Certain line voltages or line currents are shifted by a phase angle of 120.degree., while others are shifted by a phase angle of 240.degree. (which is equivalent to a phase shift of -120.degree.). After the appropriate phase shifts are made, the respective line voltages or line currents are summed to produce the negative-sequence components.
Phase shifts can be obtained with electronic components. For example, a transistor connected in a common-emitter configuration has an output voltage between its collector and emitter which is displaced 180.degree. from an input voltage applied between its base and its emitter. Phase shifts can also be obtained with passive components such as resistors and capacitors, but it is easier to obtain phase shifts between 0.degree. and .+-.90.degree. with passive components. Phase-shifting networks can be cascaded to obtain phase shifts greater than .+-.90.degree., but this is undesirable if it can be avoided.
In the application of the theory to electrical circuits, it has not always been practical or desirable to duplicate the phase shifts of the theory. Thus, the prior art devices provide several different ways to obtain a negative-sequence component. The manner in which the negative-sequence component is detected, the type of circuit response to the detected component, and the choice between monitoring line voltage and monitoring line current, have significant consequences upon the usefulness of these line monitoring devices.
In several line voltage monitoring devices in the prior art, bridge circuits are employed to detect the negative-sequence component of line voltage. Some of these circuits are limited to the utilization of passive networks of resistors and capacitors to detect a signal proportional to the negative-sequence voltage component, the object of these circuits being the elimination of inductive components. These circuits have either network configurations or impedance relationships which have been assumed on some unspecified basis other than the phase-shifting of particular signals. The devices in which these circuits are used will not prevent the starting of an electrical motor when voltage unbalance conditions are present on associated supply lines. These devices also rely on additional lockout circuits to prevent a motor from restarting after it has been disconnected due to voltage unbalance on its associated supply lines.
Other line monitoring devices employ negative-sequence current-sensing circuits. These current-sensing devices are less suitable for use in the industrial control environment because supply lines must be broken and current transformers installed therein as part of such devices. In comparison, voltage-sensing devices can usually be connected directly to the supply lines with common secondary distribution line voltages such as 208 volts, 240 volts or 480 volt. Another disadvantage of devices with current-sensing circuits is that, without added circuitry, such devices will not prevent a load from being connected under voltage unbalance conditions, because a current must be established for the operation of the current-sensing circuits.
The current-sensing devices of the prior art have employed operational amplifiers, sometimes for shifting the phase of certain currents, and sometimes for quite different purposes. Operational amplifiers can provide almost any desired phase shift, however, some phase shifts are easier to obtain than others, the easiest to obtain being a phase shift of 180.degree.. While operational amplifiers can be used to advantage in negative-sequence component detection circuits, the devices of the prior art have employed them inefficiently and in excessive numbers.